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Complete Chapter 2 answer key

Full answers and reasoning for every chapter lesson and assessment.

Print this separately when students work on assessment pages. These are publicly available explanatory solutions, not secure school answers.

Lesson 1: Mental Addition — Part 1

Entry

  1. 5000 + 700 + 30 + 5 — Break the number into the value of each nonzero place. This is a Chapter 1 decomposition skill.
  2. 900 — The hundreds digit is 9; it represents 9 hundreds, or 900 ones. This is a Chapter 1 place-value skill.

Worked checks

  1. 482 — 319 is 300 + 19; add the two parts to 163. The sum is 482.
  2. 292 — 106 is 100 + 6; add the two parts to 186. The sum is 292.
  3. 174 — 143 is 100 + 43; add the two parts to 31. The sum is 174.

Guided

  1. 466 — 273 is 200 + 73; add the two parts to 193. The sum is 466.
  2. 348 — 310 is 300 + 10; add the two parts to 38. The sum is 348.
  3. 158 — 97 is 0 + 97; add the two parts to 61. The sum is 158.
  4. 218 — 134 is 100 + 34; add the two parts to 84. The sum is 218.

Independent

  1. 2424 — 1,953 is 1,900 + 53; add the two parts to 471. The sum is 2,424.
  2. 2602 — 2,079 is 2,000 + 79; add the two parts to 523. The sum is 2,602.
  3. 2530 — 1,955 is 1,900 + 55; add the two parts to 575. The sum is 2,530.
  4. 2708 — 2,081 is 2,000 + 81; add the two parts to 627. The sum is 2,708.
  5. 2886 — 2,207 is 2,200 + 7; add the two parts to 679. The sum is 2,886.
  6. 2886 — 2,333 is 2,300 + 33; add the two parts to 553. The sum is 2,886.
  7. 1264 — 659 is 600 + 59; add the two parts to 605. The sum is 1,264.
  8. 1442 — 785 is 700 + 85; add the two parts to 657. The sum is 1,442.

Challenge

  1. Adding by place value partitions the same two quantities into parts. The sum of the parts remains 377. — 235 = 200+30+5 and 142 = 100+40+2. Combining matching units gives 300+70+7 = 377.
  2. 383 — Hundreds: 300; tens: 70; ones: 13. Exchange 13 ones as 1 ten and 3 ones, giving 300+80+3=383.

Exit

  1. 1898 — 1,553 is 1,500 + 53; add the two parts to 345. The sum is 1,898.
  2. 2076 — 1,679 is 1,600 + 79; add the two parts to 397. The sum is 2,076.
  3. 2004 — 1,555 is 1,500 + 55; add the two parts to 449. The sum is 2,004.

Lesson 2: Mental Addition — Part 2

Entry

  1. 428 — 273 is 200 + 73; add the two parts to 155. The sum is 428.
  2. 488 — 310 is 300 + 10; add the two parts to 178. The sum is 488.

Worked checks

  1. 171 — Increase 99 by 1 to get a multiple of 100; then subtract that same adjustment from the total. Result: 171.
  2. 293 — Increase 198 by 2 to get a multiple of 100; then subtract that same adjustment from the total. Result: 293.
  3. 415 — Increase 297 by 3 to get a multiple of 100; then subtract that same adjustment from the total. Result: 415.

Guided

  1. 218 — Increase 99 by 1 to get a multiple of 100; then subtract that same adjustment from the total. Result: 218.
  2. 340 — Increase 198 by 2 to get a multiple of 100; then subtract that same adjustment from the total. Result: 340.
  3. 462 — Increase 297 by 3 to get a multiple of 100; then subtract that same adjustment from the total. Result: 462.
  4. 584 — Increase 396 by 4 to get a multiple of 100; then subtract that same adjustment from the total. Result: 584.

Independent

  1. 804 — Increase 99 by 1 to get a multiple of 100; then subtract that same adjustment from the total. Result: 804.
  2. 777 — Increase 198 by 2 to get a multiple of 100; then subtract that same adjustment from the total. Result: 777.
  3. 928 — Increase 297 by 3 to get a multiple of 100; then subtract that same adjustment from the total. Result: 928.
  4. 1079 — Increase 396 by 4 to get a multiple of 100; then subtract that same adjustment from the total. Result: 1,079.
  5. 776 — Increase 491 by 9 to get a multiple of 100; then subtract that same adjustment from the total. Result: 776.
  6. 436 — Increase 99 by 1 to get a multiple of 100; then subtract that same adjustment from the total. Result: 436.
  7. 587 — Increase 198 by 2 to get a multiple of 100; then subtract that same adjustment from the total. Result: 587.
  8. 738 — Increase 297 by 3 to get a multiple of 100; then subtract that same adjustment from the total. Result: 738.

Challenge

  1. 455 — Raising 398 to 400 adds 2 extra, so 400+57−2=455.
  2. Less by 3 — Replacing 497 by 500 adds three, so the original sum is exactly three less.

Exit

  1. 678 — Increase 99 by 1 to get a multiple of 100; then subtract that same adjustment from the total. Result: 678.
  2. 829 — Increase 198 by 2 to get a multiple of 100; then subtract that same adjustment from the total. Result: 829.
  3. 802 — Increase 297 by 3 to get a multiple of 100; then subtract that same adjustment from the total. Result: 802.

Lesson 3: Mental Subtraction — Part 1

Entry

  1. 3000 + 400 + 10 + 5 — Break the number into the value of each nonzero place. This is a Chapter 1 decomposition skill.
  2. 100 — The hundreds digit is 1; it represents 1 hundreds, or 100 ones. This is a Chapter 1 place-value skill.

Worked checks

  1. 417 — Decompose 159 into tens and ones, subtract each part from 576, and check the difference 417.
  2. 204 — Decompose 182 into tens and ones, subtract each part from 386, and check the difference 204.
  3. 241 — Decompose 27 into tens and ones, subtract each part from 268, and check the difference 241.

Guided

  1. 353 — Decompose 45 into tens and ones, subtract each part from 398, and check the difference 353.
  2. 390 — Decompose 68 into tens and ones, subtract each part from 458, and check the difference 390.
  3. 427 — Decompose 91 into tens and ones, subtract each part from 518, and check the difference 427.
  4. 214 — Decompose 114 into tens and ones, subtract each part from 328, and check the difference 214.

Independent

  1. 1993 — Decompose 311 into tens and ones, subtract each part from 2,304, and check the difference 1,993.
  2. 2119 — Decompose 363 into tens and ones, subtract each part from 2,482, and check the difference 2,119.
  3. 2245 — Decompose 415 into tens and ones, subtract each part from 2,660, and check the difference 2,245.
  4. 2121 — Decompose 467 into tens and ones, subtract each part from 2,588, and check the difference 2,121.
  5. 2247 — Decompose 341 into tens and ones, subtract each part from 2,588, and check the difference 2,247.
  6. 2373 — Decompose 393 into tens and ones, subtract each part from 2,766, and check the difference 2,373.
  7. 2499 — Decompose 445 into tens and ones, subtract each part from 2,944, and check the difference 2,499.
  8. 825 — Decompose 497 into tens and ones, subtract each part from 1,322, and check the difference 825.

Challenge

  1. 303 — Subtracting 200 removes 3 too many. Return 3 to obtain 303.
  2. 543, 493, 485 — 743−200=543; 543−50=493; 493−8=485. Each subtraction is part of the same 258.

Exit

  1. 1593 — Decompose 635 into tens and ones, subtract each part from 2,228, and check the difference 1,593.
  2. 1719 — Decompose 687 into tens and ones, subtract each part from 2,406, and check the difference 1,719.
  3. 1845 — Decompose 739 into tens and ones, subtract each part from 2,584, and check the difference 1,845.

Lesson 4: Mental Subtraction — Part 2

Entry

  1. 363 — Decompose 81 into tens and ones, subtract each part from 444, and check the difference 363.
  2. 400 — Decompose 104 into tens and ones, subtract each part from 504, and check the difference 400.

Worked checks

  1. 173 — Add 2 to BOTH numbers: 373 − 200 = 173. Their difference is unchanged.
  2. 220 — Add 3 to BOTH numbers: 520 − 300 = 220. Their difference is unchanged.
  3. 267 — Add 4 to BOTH numbers: 667 − 400 = 267. Their difference is unchanged.

Guided

  1. 410 — Add 1 to BOTH numbers: 510 − 100 = 410. Their difference is unchanged.
  2. 457 — Add 2 to BOTH numbers: 657 − 200 = 457. Their difference is unchanged.
  3. 154 — Add 3 to BOTH numbers: 454 − 300 = 154. Their difference is unchanged.
  4. 201 — Add 4 to BOTH numbers: 601 − 400 = 201. Their difference is unchanged.

Independent

  1. 260 — Add 1 to BOTH numbers: 360 − 100 = 260. Their difference is unchanged.
  2. 307 — Add 2 to BOTH numbers: 507 − 200 = 307. Their difference is unchanged.
  3. 354 — Add 3 to BOTH numbers: 654 − 300 = 354. Their difference is unchanged.
  4. 401 — Add 4 to BOTH numbers: 801 − 400 = 401. Their difference is unchanged.
  5. 448 — Add 1 to BOTH numbers: 548 − 100 = 448. Their difference is unchanged.
  6. 495 — Add 2 to BOTH numbers: 695 − 200 = 495. Their difference is unchanged.
  7. 192 — Add 3 to BOTH numbers: 492 − 300 = 192. Their difference is unchanged.
  8. 239 — Add 4 to BOTH numbers: 639 − 400 = 239. Their difference is unchanged.

Challenge

  1. No — 505−198=307, not 305. To preserve the difference also change 198 to 200.
  2. 693 − 300 = 393 — Add two to both numbers; the distance between them does not change.

Exit

  1. 310 — Add 1 to BOTH numbers: 410 − 100 = 310. Their difference is unchanged.
  2. 357 — Add 2 to BOTH numbers: 557 − 200 = 357. Their difference is unchanged.
  3. 404 — Add 3 to BOTH numbers: 704 − 300 = 404. Their difference is unchanged.

Lesson 5: Making 100 and Making 1,000

Entry

  1. 233 — Decompose 133 into tens and ones, subtract each part from 366, and check the difference 233.
  2. 270 — Decompose 156 into tens and ones, subtract each part from 426, and check the difference 270.

Worked checks

  1. 50 — The missing part is 100 − 50 = 50; check 50 + 50 = 100.
  2. 898 — The missing part is 1,000 − 102 = 898; check 102 + 898 = 1,000.
  3. 46 — The missing part is 100 − 54 = 46; check 54 + 46 = 100.

Guided

  1. 42 — The missing part is 100 − 58 = 42; check 58 + 42 = 100.
  2. 730 — The missing part is 1,000 − 270 = 730; check 270 + 730 = 1,000.
  3. 58 — The missing part is 100 − 42 = 58; check 42 + 58 = 100.
  4. 906 — The missing part is 1,000 − 94 = 906; check 94 + 906 = 1,000.

Independent

  1. 62 — The missing part is 100 − 38 = 62; check 38 + 62 = 100.
  2. 41 — The missing part is 1,000 − 959 = 41; check 959 + 41 = 1,000.
  3. 80 — The missing part is 100 − 20 = 80; check 20 + 80 = 100.
  4. 39 — The missing part is 1,000 − 961 = 39; check 961 + 39 = 1,000.
  5. 78 — The missing part is 100 − 22 = 78; check 22 + 78 = 100.
  6. 787 — The missing part is 1,000 − 213 = 787; check 213 + 787 = 1,000.
  7. 6 — The missing part is 100 − 94 = 6; check 94 + 6 = 100.
  8. 335 — The missing part is 1,000 − 665 = 335; check 665 + 335 = 1,000.

Challenge

  1. 214 — 786→800 is 14 and 800→1,000 is 200. Together 214.
  2. 313 cm — 687→700 uses 13 cm, then 700→1,000 uses 300 cm, totaling 313 cm.

Exit

  1. 12 — The missing part is 100 − 88 = 12; check 88 + 12 = 100.
  2. 441 — The missing part is 1,000 − 559 = 441; check 559 + 441 = 1,000.
  3. 30 — The missing part is 100 − 70 = 30; check 70 + 30 = 100.

Lesson 6: Strategies for Numbers Close to Hundreds

Entry

  1. 284 — Increase 99 by 1 to get a multiple of 100; then subtract that same adjustment from the total. Result: 284.
  2. 228 — Increase 198 by 2 to get a multiple of 100; then subtract that same adjustment from the total. Result: 228.

Worked checks

  1. 866 — Rewrite 402 as the nearby multiple of 100 with a small correction. Apply the correction to 464 and check the exact answer 866.
  2. 754 — Rewrite 503 as the nearby multiple of 100 with a small correction. Apply the correction to 251 and check the exact answer 754.
  3. 386 — Rewrite 98 as the nearby multiple of 100 with a small correction. Apply the correction to 288 and check the exact answer 386.

Guided

  1. 275 — Rewrite 98 as the nearby multiple of 100 with a small correction. Apply the correction to 373 and check the exact answer 275.
  2. 609 — Rewrite 199 as the nearby multiple of 100 with a small correction. Apply the correction to 410 and check the exact answer 609.
  3. 146 — Rewrite 301 as the nearby multiple of 100 with a small correction. Apply the correction to 447 and check the exact answer 146.
  4. 636 — Rewrite 402 as the nearby multiple of 100 with a small correction. Apply the correction to 234 and check the exact answer 636.

Independent

  1. 1855 — Rewrite 98 as the nearby multiple of 100 with a small correction. Apply the correction to 1,953 and check the exact answer 1,855.
  2. 2278 — Rewrite 199 as the nearby multiple of 100 with a small correction. Apply the correction to 2,079 and check the exact answer 2,278.
  3. 1904 — Rewrite 301 as the nearby multiple of 100 with a small correction. Apply the correction to 2,205 and check the exact answer 1,904.
  4. 2483 — Rewrite 402 as the nearby multiple of 100 with a small correction. Apply the correction to 2,081 and check the exact answer 2,483.
  5. 1704 — Rewrite 503 as the nearby multiple of 100 with a small correction. Apply the correction to 2,207 and check the exact answer 1,704.
  6. 2431 — Rewrite 98 as the nearby multiple of 100 with a small correction. Apply the correction to 2,333 and check the exact answer 2,431.
  7. 2260 — Rewrite 199 as the nearby multiple of 100 with a small correction. Apply the correction to 2,459 and check the exact answer 2,260.
  8. 1086 — Rewrite 301 as the nearby multiple of 100 with a small correction. Apply the correction to 785 and check the exact answer 1,086.

Challenge

  1. 303 — 602−300=302; since 299 is one less than 300, add one back: 303.
  2. 1,000 — 800+243−1=1,042. It is 42 from 1,000 and 58 from 1,100.

Exit

  1. 1455 — Rewrite 98 as the nearby multiple of 100 with a small correction. Apply the correction to 1,553 and check the exact answer 1,455.
  2. 1878 — Rewrite 199 as the nearby multiple of 100 with a small correction. Apply the correction to 1,679 and check the exact answer 1,878.
  3. 1504 — Rewrite 301 as the nearby multiple of 100 with a small correction. Apply the correction to 1,805 and check the exact answer 1,504.

Lesson 7: Sum and Difference

Entry

  1. 223 — Decompose 59 into tens and ones, subtract each part from 282, and check the difference 223.
  2. 260 — Decompose 82 into tens and ones, subtract each part from 342, and check the difference 260.

Worked checks

  1. 40 and 90 — Remove the extra 50; 130 − 50 = 80. Two equal parts are 40 each. Larger part is 40 + 50 = 90.
  2. 53 and 117 — Remove the extra 64; 170 − 64 = 106. Two equal parts are 53 each. Larger part is 53 + 64 = 117.
  3. 66 and 84 — Remove the extra 18; 150 − 18 = 132. Two equal parts are 66 each. Larger part is 66 + 18 = 84.

Guided

  1. 70 and 120 — Remove the extra 50; 190 − 50 = 140. Two equal parts are 70 each. Larger part is 70 + 50 = 120.
  2. 83 and 147 — Remove the extra 64; 230 − 64 = 166. Two equal parts are 83 each. Larger part is 83 + 64 = 147.
  3. 96 and 114 — Remove the extra 18; 210 − 18 = 192. Two equal parts are 96 each. Larger part is 96 + 18 = 114.
  4. 109 and 141 — Remove the extra 32; 250 − 32 = 218. Two equal parts are 109 each. Larger part is 109 + 32 = 141.

Independent

  1. 40 and 70 — Remove the extra 30; 110 − 30 = 80. Two equal parts are 40 each. Larger part is 40 + 30 = 70.
  2. 53 and 97 — Remove the extra 44; 150 − 44 = 106. Two equal parts are 53 each. Larger part is 53 + 44 = 97.
  3. 66 and 124 — Remove the extra 58; 190 − 58 = 132. Two equal parts are 66 each. Larger part is 66 + 58 = 124.
  4. 79 and 91 — Remove the extra 12; 170 − 12 = 158. Two equal parts are 79 each. Larger part is 79 + 12 = 91.
  5. 92 and 118 — Remove the extra 26; 210 − 26 = 184. Two equal parts are 92 each. Larger part is 92 + 26 = 118.
  6. 105 and 145 — Remove the extra 40; 250 − 40 = 210. Two equal parts are 105 each. Larger part is 105 + 40 = 145.
  7. 23 and 77 — Remove the extra 54; 100 − 54 = 46. Two equal parts are 23 each. Larger part is 23 + 54 = 77.
  8. 36 and 104 — Remove the extra 68; 140 − 68 = 72. Two equal parts are 36 each. Larger part is 36 + 68 = 104.

Challenge

  1. 29 and 44 — Remove difference 15: 73−15=58; split in two equal integer parts of 29, then add 15 to find 44.
  2. Difference becomes 0 — The transfer decreases one amount by 9 and increases the other by 9, decreasing the difference by 18.

Exit

  1. 75 and 125 — Remove the extra 50; 200 − 50 = 150. Two equal parts are 75 each. Larger part is 75 + 50 = 125.
  2. 88 and 152 — Remove the extra 64; 240 − 64 = 176. Two equal parts are 88 each. Larger part is 88 + 64 = 152.
  3. 101 and 119 — Remove the extra 18; 220 − 18 = 202. Two equal parts are 101 each. Larger part is 101 + 18 = 119.

Lesson 8: Word Problems — Part 1

Entry

  1. 32 — The missing part is 100 − 68 = 32; check 68 + 32 = 100.
  2. 720 — The missing part is 1,000 − 280 = 720; check 280 + 720 = 1,000.

Worked checks

  1. 18 — The 197 books are the whole, 179 is a part. Subtract: 197 − 179 = 18.
  2. 42 — The 238 books are the whole, 196 is a part. Subtract: 238 − 196 = 42.
  3. 66 — The 279 books are the whole, 213 is a part. Subtract: 279 − 213 = 66.

Guided

  1. 390 — The 460 books are the whole, 70 is a part. Subtract: 460 − 70 = 390.
  2. 414 — The 501 books are the whole, 87 is a part. Subtract: 501 − 87 = 414.
  3. 438 — The 542 books are the whole, 104 is a part. Subtract: 542 − 104 = 438.
  4. 462 — The 583 books are the whole, 121 is a part. Subtract: 583 − 121 = 462.

Independent

  1. 560 — The 620 books are the whole, 60 is a part. Subtract: 620 − 60 = 560.
  2. 584 — The 661 books are the whole, 77 is a part. Subtract: 661 − 77 = 584.
  3. 608 — The 702 books are the whole, 94 is a part. Subtract: 702 − 94 = 608.
  4. 632 — The 743 books are the whole, 111 is a part. Subtract: 743 − 111 = 632.
  5. 656 — The 784 books are the whole, 128 is a part. Subtract: 784 − 128 = 656.
  6. 60 — The 205 books are the whole, 145 is a part. Subtract: 205 − 145 = 60.
  7. 84 — The 246 books are the whole, 162 is a part. Subtract: 246 − 162 = 84.
  8. 108 — The 287 books are the whole, 179 is a part. Subtract: 287 − 179 = 108.

Challenge

  1. Students who did not go on the trip — 28−11=17 is the other part of the class, not 17 additional students.
  2. 24 seedlings — Known parts total 18+21=39; third part 63−39=24. Three-part whole model: 18, 21, 24.

Exit

  1. 280 — The 320 books are the whole, 40 is a part. Subtract: 320 − 40 = 280.
  2. 304 — The 361 books are the whole, 57 is a part. Subtract: 361 − 57 = 304.
  3. 328 — The 402 books are the whole, 74 is a part. Subtract: 402 − 74 = 328.

Lesson 9: Word Problems — Part 2

Entry

  1. 490 — The 610 books are the whole, 120 is a part. Subtract: 610 − 120 = 490.
  2. 514 — The 651 books are the whole, 137 is a part. Subtract: 651 − 137 = 514.

Worked checks

  1. 475 — Draw Leo’s bar of 409; add the extra segment 66. Mina’s total is 409+66=475.
  2. 515 — Draw Leo’s bar of 440; add the extra segment 75. Mina’s total is 440+75=515.
  3. 555 — Draw Leo’s bar of 471; add the extra segment 84. Mina’s total is 471+84=555.

Guided

  1. 185 — Draw Leo’s bar of 105; add the extra segment 80. Mina’s total is 105+80=185.
  2. 225 — Draw Leo’s bar of 136; add the extra segment 89. Mina’s total is 136+89=225.
  3. 265 — Draw Leo’s bar of 167; add the extra segment 98. Mina’s total is 167+98=265.
  4. 305 — Draw Leo’s bar of 198; add the extra segment 107. Mina’s total is 198+107=305.

Independent

  1. 205 — Draw Leo’s bar of 165; add the extra segment 40. Mina’s total is 165+40=205.
  2. 245 — Draw Leo’s bar of 196; add the extra segment 49. Mina’s total is 196+49=245.
  3. 285 — Draw Leo’s bar of 227; add the extra segment 58. Mina’s total is 227+58=285.
  4. 325 — Draw Leo’s bar of 258; add the extra segment 67. Mina’s total is 258+67=325.
  5. 365 — Draw Leo’s bar of 289; add the extra segment 76. Mina’s total is 289+76=365.
  6. 405 — Draw Leo’s bar of 320; add the extra segment 85. Mina’s total is 320+85=405.
  7. 445 — Draw Leo’s bar of 351; add the extra segment 94. Mina’s total is 351+94=445.
  8. 485 — Draw Leo’s bar of 382; add the extra segment 103. Mina’s total is 382+103=485.

Challenge

  1. 12 is the difference, not the total — Mira has Leo’s quantity PLUS an extra 12; Mira’s total cannot be known without Leo’s quantity.
  2. 106 chairs — 145−39=106. Hall B is 39 fewer, so its bar is shorter by a 39-chair segment.

Exit

  1. 355 — Draw Leo’s bar of 285; add the extra segment 70. Mina’s total is 285+70=355.
  2. 395 — Draw Leo’s bar of 316; add the extra segment 79. Mina’s total is 316+79=395.
  3. 435 — Draw Leo’s bar of 347; add the extra segment 88. Mina’s total is 347+88=435.

Lesson 10: 2-Step Word Problems

Entry

  1. 485 — Draw Leo’s bar of 445; add the extra segment 40. Mina’s total is 445+40=485.
  2. 525 — Draw Leo’s bar of 476; add the extra segment 49. Mina’s total is 476+49=525.

Worked checks

  1. 173 — First 117+73=190; then take away 17. Result: 173.
  2. 226 — First 174+86=260; then take away 34. Result: 226.
  3. 279 — First 231+99=330; then take away 51. Result: 279.

Guided

  1. 320 — First 330+40=370; then take away 50. Result: 320.
  2. 373 — First 387+53=440; then take away 67. Result: 373.
  3. 166 — First 124+66=190; then take away 24. Result: 166.
  4. 219 — First 181+79=260; then take away 41. Result: 219.

Independent

  1. 410 — First 410+30=440; then take away 30. Result: 410.
  2. 143 — First 147+43=190; then take away 47. Result: 143.
  3. 196 — First 204+56=260; then take away 64. Result: 196.
  4. 309 — First 261+69=330; then take away 21. Result: 309.
  5. 362 — First 318+82=400; then take away 38. Result: 362.
  6. 415 — First 375+95=470; then take away 55. Result: 415.
  7. 208 — First 112+108=220; then take away 12. Result: 208.
  8. 171 — First 169+31=200; then take away 29. Result: 171.

Challenge

  1. 127 — 120+45=165 before lending. 165−38=127 because the final change occurs after receipt.
  2. 305 boxes; no — 280−65+90=305 and 280+90−65=305. Both orders work here because only additions/subtractions of fixed quantities occur, with no further restrictions.

Exit

  1. 300 — First 250+100=350; then take away 50. Result: 300.
  2. 263 — First 307+23=330; then take away 67. Result: 263.
  3. 376 — First 364+36=400; then take away 24. Result: 376.

Practice A

Solutions

  1. 2348 — 2,003 is 2,000 + 3; add the two parts to 345. The sum is 2,348.
  2. 2526 — 2,129 is 2,100 + 29; add the two parts to 397. The sum is 2,526.
  3. 2526 — 2,255 is 2,200 + 55; add the two parts to 271. The sum is 2,526.
  4. 500 — Increase 99 by 1 to get a multiple of 100; then subtract that same adjustment from the total. Result: 500.
  5. 651 — Increase 198 by 2 to get a multiple of 100; then subtract that same adjustment from the total. Result: 651.
  6. 802 — Increase 297 by 3 to get a multiple of 100; then subtract that same adjustment from the total. Result: 802.
  7. 2043 — Decompose 635 into tens and ones, subtract each part from 2,678, and check the difference 2,043.
  8. 2169 — Decompose 509 into tens and ones, subtract each part from 2,678, and check the difference 2,169.
  9. 2295 — Decompose 561 into tens and ones, subtract each part from 2,856, and check the difference 2,295.
  10. 410 — Add 1 to BOTH numbers: 510 − 100 = 410. Their difference is unchanged.
  11. 457 — Add 2 to BOTH numbers: 657 − 200 = 457. Their difference is unchanged.
  12. 154 — Add 3 to BOTH numbers: 454 − 300 = 154. Their difference is unchanged.
  13. 12 — The missing part is 100 − 88 = 12; check 88 + 12 = 100.
  14. 991 — The missing part is 1,000 − 9 = 991; check 9 + 991 = 1,000.
  15. 30 — The missing part is 100 − 70 = 30; check 70 + 30 = 100.
  16. 1905 — Rewrite 98 as the nearby multiple of 100 with a small correction. Apply the correction to 2,003 and check the exact answer 1,905.
  17. 2328 — Rewrite 199 as the nearby multiple of 100 with a small correction. Apply the correction to 2,129 and check the exact answer 2,328.
  18. 1954 — Rewrite 301 as the nearby multiple of 100 with a small correction. Apply the correction to 2,255 and check the exact answer 1,954.

Practice B

Solutions

  1. 1905 — Rewrite 98 as the nearby multiple of 100 with a small correction. Apply the correction to 2,003 and check the exact answer 1,905.
  2. 2328 — Rewrite 199 as the nearby multiple of 100 with a small correction. Apply the correction to 2,129 and check the exact answer 2,328.
  3. 1954 — Rewrite 301 as the nearby multiple of 100 with a small correction. Apply the correction to 2,255 and check the exact answer 1,954.
  4. 95 and 105 — Remove the extra 10; 200 − 10 = 190. Two equal parts are 95 each. Larger part is 95 + 10 = 105.
  5. 108 and 132 — Remove the extra 24; 240 − 24 = 216. Two equal parts are 108 each. Larger part is 108 + 24 = 132.
  6. 26 and 64 — Remove the extra 38; 90 − 38 = 52. Two equal parts are 26 each. Larger part is 26 + 38 = 64.
  7. 210 — The 320 books are the whole, 110 is a part. Subtract: 320 − 110 = 210.
  8. 234 — The 361 books are the whole, 127 is a part. Subtract: 361 − 127 = 234.
  9. 258 — The 402 books are the whole, 144 is a part. Subtract: 402 − 144 = 258.
  10. 275 — Draw Leo’s bar of 245; add the extra segment 30. Mina’s total is 245+30=275.
  11. 315 — Draw Leo’s bar of 276; add the extra segment 39. Mina’s total is 276+39=315.
  12. 355 — Draw Leo’s bar of 307; add the extra segment 48. Mina’s total is 307+48=355.
  13. 380 — First 310+80=390; then take away 10. Result: 380.
  14. 433 — First 367+93=460; then take away 27. Result: 433.
  15. 486 — First 424+106=530; then take away 44. Result: 486.

Chapter Review

Solutions

  1. 1124 — 689 is 600 + 89; add the two parts to 435. The sum is 1,124.
  2. 732 — Increase 297 by 3 to get a multiple of 100; then subtract that same adjustment from the total. Result: 732.
  3. 1464 — Rewrite 301 as the nearby multiple of 100 with a small correction. Apply the correction to 1,765 and check the exact answer 1,464.
  4. 255 — Draw Leo’s bar of 146; add the extra segment 109. Mina’s total is 146+109=255.
  5. 1302 — 815 is 800 + 15; add the two parts to 487. The sum is 1,302.
  6. 216 — First 204+36=240; then take away 24. Result: 216.
  7. 608 — Increase 99 by 1 to get a multiple of 100; then subtract that same adjustment from the total. Result: 608.
  8. 287 — Add 2 to BOTH numbers: 487 − 200 = 287. Their difference is unchanged.
  9. 603 — 725−200+2+76=603.
  10. 52 and 66 — Remove extra 14, divide the remaining 104 by 2 to find 52; larger is 66.
  11. 103 and 167 — Remove the extra 64; 270 − 64 = 206. Two equal parts are 103 each. Larger part is 103 + 64 = 167.
  12. 825 — Decompose 561 into tens and ones, subtract each part from 1,386, and check the difference 825.
  13. 460 — First 410+100=510; then take away 50. Result: 460.
  14. 92 — The missing part is 100 − 8 = 92; check 8 + 92 = 100.
  15. 80 — The 200 books are the whole, 120 is a part. Subtract: 200 − 120 = 80.
  16. 1838 — Rewrite 199 as the nearby multiple of 100 with a small correction. Apply the correction to 1,639 and check the exact answer 1,838.
  17. 128 — The 282 books are the whole, 154 is a part. Subtract: 282 − 154 = 128.
  18. 823 — Decompose 457 into tens and ones, subtract each part from 1,280, and check the difference 823.
  19. 1124 — 563 is 500 + 63; add the two parts to 561. The sum is 1,124.
  20. 307 — 504−200+3=307; the child failed to return the 3.
  21. 699 — Decompose 509 into tens and ones, subtract each part from 1,208, and check the difference 699.
  22. 103 — First 147+23=170; then take away 67. Result: 103.
  23. 759 — Increase 198 by 2 to get a multiple of 100; then subtract that same adjustment from the total. Result: 759.
  24. 90 — The missing part is 100 − 10 = 90; check 10 + 90 = 100.
  25. 90 and 140 — Remove the extra 50; 230 − 50 = 180. Two equal parts are 90 each. Larger part is 90 + 50 = 140.
  26. 241 — The missing part is 1,000 − 759 = 241; check 759 + 241 = 1,000.
  27. 21 and 39 — Remove the extra 18; 60 − 18 = 42. Two equal parts are 21 each. Larger part is 21 + 18 = 39.
  28. 1415 — Rewrite 98 as the nearby multiple of 100 with a small correction. Apply the correction to 1,513 and check the exact answer 1,415.
  29. 400 — Grouping the same addends in a different way preserves the total; 57+43=100.
  30. 104 — The 241 books are the whole, 137 is a part. Subtract: 241 − 137 = 104.
  31. 215 — Draw Leo’s bar of 115; add the extra segment 100. Mina’s total is 115+100=215.
  32. 334 — Add 3 to BOTH numbers: 634 − 300 = 334. Their difference is unchanged.
  33. 295 — Draw Leo’s bar of 177; add the extra segment 118. Mina’s total is 177+118=295.
  34. 240 — Add 1 to BOTH numbers: 340 − 100 = 240. Their difference is unchanged.

Practice Exam

Solutions

  1. 500−197 by 6 — A smaller subtrahend leaves a larger difference. Since 203−197=6, the second expression is six larger.
  2. 2398 — 1,963 is 1,900 + 63; add the two parts to 435. The sum is 2,398.
  3. 175 — 214+86=300; 300−125=175.
  4. Equal adjustment — Adding one to both terms leaves their difference 308 unchanged.
  5. 420 — The 520 books are the whole, 100 is a part. Subtract: 520 − 100 = 420.
  6. 482 — Increase 99 by 1 to get a multiple of 100; then subtract that same adjustment from the total. Result: 482.
  7. 30 and 40 — Remove the extra 10; 70 − 10 = 60. Two equal parts are 30 each. Larger part is 30 + 10 = 40.
  8. 602 — 1,000−398=602; 398+602=1,000.
  9. 66 — The gain of 31 exceeds the loss of 19 by 12, so final amount is 66.
  10. 84 — Ari’s bar is 48 shorter: 132−48=84.
  11. 645 — Replacing 498 by 500 adds two, so subtract two: 647−2=645.
  12. 39 and 55 — 94−16=78; half is 39; other box 39+16=55.
  13. 290 — Add 1 to BOTH numbers: 390 − 100 = 290. Their difference is unchanged.
  14. The parts are unchanged — Regrouping/reordering the same place-value contributions does not alter the total.
  15. 2223 — Decompose 331 into tens and ones, subtract each part from 2,554, and check the difference 2,223.
  16. 255 — Draw Leo’s bar of 235; add the extra segment 20. Mina’s total is 235+20=255.
  17. 403 — 200−5 + 200+8 = 400+3=403.
  18. 40 — Smaller jar is 120−80=40; difference 80−40=40.
  19. 320 — First 250+80=330; then take away 10. Result: 320.
  20. 1015 — Rewrite 98 as the nearby multiple of 100 with a small correction. Apply the correction to 1,113 and check the exact answer 1,015.
  21. 42 — The missing part is 100 − 58 = 42; check 58 + 42 = 100.
  22. 223 — 256−79=177; 177+46=223.